Question: Solve for $x$ and $y$ using elimination. ${-3x+6y = 21}$ ${5x+3y = 43}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-3x+6y = 21}$ $-10x-6y = -86$ Add the top and bottom equations together. $-13x = -65$ $\dfrac{-13x}{{-13}} = \dfrac{-65}{{-13}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-3x+6y = 21}\thinspace$ to find $y$ ${-3}{(5)}{ + 6y = 21}$ $-15+6y = 21$ $-15{+15} + 6y = 21{+15}$ $6y = 36$ $\dfrac{6y}{{6}} = \dfrac{36}{{6}}$ ${y = 6}$ You can also plug ${x = 5}$ into $\thinspace {5x+3y = 43}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ + 3y = 43}$ ${y = 6}$